Abstract
It is known that every 3-dimensional noetherian Calabi–Yau algebra generated in degree 1 is isomorphic to a Jacobian algebra of a superpotential. Recently, S.P. Smith and the first author classified all superpotentials whose Jacobian algebras are 3-dimensional noetherian quadratic Calabi–Yau algebras. The main result of this paper is to classify all superpotentials whose Jacobian algebras are 3-dimensional noetherian cubic Calabi–Yau algebras. As an application, we show that if S is a 3-dimensional noetherian cubic Calabi–Yau algebra and σ is a graded algebra automorphism of S, then the homological determinant of σ can be calculated by the formula hdetσ=(detσ)2 with one exception.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
